**Sutao Han 1, Xuedao Shu 1,2,\* and Chang Shu <sup>3</sup>**


Received: 30 June 2018; Accepted: 18 July 2018; Published: 25 July 2018

**Abstract:** Considering problems about concaves at the stepped shaft ends, this paper established the plastic flow kinetic theories about metal deforming during the cross-wedge rolling (CWR) process. By means of the DEFORM-3D finite element software and the point tracing method, the forming process of stepped shafts and the forming mechanism of concaves at shaft ends were studied. Based on the forming features of stepped shafts, rolling pieces were designed using variable cone angle billets. Single-factor tests were conducted to analyze the influence law of the shape parameters of billet with variable cone angle on end concaves, and rolling experiments were performed for verification. According to the results, during the rolling process of stepped shafts, concaves will come into being in stages, and the increasing tendency of its depth is due to the wave mode, the parameters of cone angle α, the first cone section length **n**. Furthermore, the total cone section length **m** has an increasingly weaker influence on the end concaves. Specifically, cone angle α has the most significant influence on the quality of shaft ends, which is about twice the influence of the total cone section length **m**. The concave depth will decrease at the beginning, and then increase with the increasing of the cone angle α and the first cone section length **n**, and it will decrease with the increasing of the total cone section length **m**. Finite element numerical analysis results are perfectly consistent with experimental results, with the error ratio being lower than 5%. The results provide a reliable theoretical basis for effectively disposing of end concave problems during CWR, rationally confirming the shape parameters of billets with a variable cone angle, improving the quality of stepped shaft ends, and realizing the near-net forming process of cross-wedge rolling without a stub bar.

**Keywords:** stepped shaft; cross wedge rolling; plastic flow kinetic theories; variable cone angle billets; near-net forming
